When a director demands the ability to make the final go/no-go decision about whether the systems go live, the project manager should schedule a meeting with the project sponsor to determine if it is appropriate to accept the director's request. The project sponsor is typically a senior executive in a corporation (often at or just below board level) who is responsible to the business for the success of the project. This meeting would help clarify roles and responsibilities, and ensure that the decision-making process aligns with the project's governance structure. References:
https://www.coursera.org/articles/project-management-lifecycle
https://www.projectmanager.com/blog/project-director-role